Epistemology-Inspired Bayesian Games for Distributed IoT Uplink Power Control

TL;DR

This work tackles scalable uplink power control for densely deployed IoT devices under incomplete CSI by introducing an epistemology-inspired Bayesian game. The core idea is to replace exhaustive expected-utility tables with inter-/intra-epistemic belief updates, leveraging an exponential–Gamma SINR model and augmenting utilities with higher-order moments to better capture heavy-tailed interference. The framework achieves a computationally lean upper bound of $O\left(N^{2} S^{2N}\right)$ per allocation realization and demonstrates that fourth-moment (and other moment) policies can substantially reduce average transmit power while maintaining reliable coverage under strong interference. The approach yields precise power control and improved network coverage in realistic, uncertain dense IoT networks, offering a principled path toward distributed, interference-aware resource allocation on low-power devices.

Abstract

Massive number of simultaneous Internet of Things (IoT) uplinks strain gateways with interference and energy limits, yet devices often lack neighbors' Channel State Information (CSI) and cannot sustain centralized Mobile Edge Computing (MEC) or heavy Machine Learning (ML) coordination. Classical Bayesian solvers help with uncertainty but become intractable as users and strategies grow, making lightweight, distributed control essential. In this paper, we introduce the first-ever, novel epistemic Bayesian game for uplink power control under incomplete CSI that operates while suppressing interference among multiple uplink channels from distributed IoT devices firing at the same time. Nodes run inter-/intra-epistemic belief updates over opponents' strategies, replacing exhaustive expected-utility tables with conditional belief hierarchies. Using an exponential-Gamma SINR model and higher-order utility moments (variance, skewness, kurtosis), the scheme remains computationally lean with a single-round upper bound of $O\!\left(N^{2} S^{2N}\right)$. Precise power control and stronger coverage amid realistic interference: with channel magnitude equal to $1$ and a signal-to-interference-plus-noise ratio (SINR) threshold of $-18$ dB, coverage reaches approximately $60\%$ at approximately $55\%$ of the maximum transmit power; mid-rate devices with a threshold of $-27$ dB achieve full coverage with less than $0.1\%$ of the maximum transmit power.Under $80\%$ interference, a fourth-moment policy cuts average power from approximately $52\%$ to approximately $20\%$ of the maximum transmit power with comparable outage, outperforming expectation-only baselines. These results highlight a principled, computationally lean path to optimal power allocation and higher network coverage under real-world uncertainty within dense, distributed IoT networks.

Figures (6)

• Figure 1: Conceptual representation of Epistemic Bayesian Game Model with inter and intra epistemic decision-making approach.
• Figure 2: Visualization ($3D$ Schematic) of normalized transmit power strategy convergence pattern toward the equilibrium for $2$ IoT nodes, named $i$ and $j$, with CSI $\left| g_{i} \right| =0.2$ and $\left| g_{j} \right|=0.1$ satisfying the given channel throughput threshold values (linear) $\gamma_{i}= 0.8$ and $\gamma_{j}=0.4$.
• Figure 3: Variation of Normalized average transmit power $(\bar{P}_{tx,i} \text{ Vs } \left| g_{i} \right|)$ of the desired IoT node $i$, against Rayleigh channel gain with unity average power for given SINR threshold $\gamma_{i}^{th}$ values.
• Figure 4: Variation of Normalized coverage probability $(\Pr_{cov} \text{ Vs } \left| g_{i} \right|)$, of the desired IoT node $i$, against Rayleigh channel gain with unity average power for given SINR threshold $\gamma_{i}^{th}$ values.
• Figure 5: Performance comparison of coverage probability $(\Pr_{out} \text{ Vs } j\% )$ of the IoT network $i \in \mathcal{N}$, against the interference strength $j\%$ with Rayleigh channel gain with unity average power for the set of HoS $M_{k, \gamma_{i}}$ values of SINR $\gamma_{i}$ bounded by $\gamma_{i}^{th}=-20\,\mathrm{dB}$ then the baselines of EPA and S-NCPC.